Civil Engineering Reference
In-Depth Information
Using the EC3 simple general method with
β
=
1.0,
λ
LT
,0
=
0.2 (Clause 6.3.2.2)
and
α
LT
=
0.34 (Tables 6.4 and 6.3), and equation 6.27,
Φ
LT
=
0.5
{
1
+
0.34
(
0.629
−
0.2
)
+
1.0
×
0.629
2
}=
0.771
Using equation 6.26,
M
b
,
Rd
=
503.5
/
{
0.771
+
√
(
0.771
2
−
0.629
2
)
}
kNm
=
414kNm
<
433kNm
=
M
Ed
and the beam appears to be inadequate.
Using the EC3 less conservative method with
β
=
0.75,
λ
LT
,0
=
0.4 (Clause
6.3.2.3) and
α
LT
=
0.49 (Tables 6.5 and 6.3), and equation 6.27,
Φ
LT
=
0.5
{
1
+
0.49
(
0.629
−
0.4
)
+
0.75
×
0.629
2
}=
0.704
Using equation 6.26,
M
b
,
Rd
=
503.5
/
{
0.704
+
√
(
0.704
2
−
0.75
×
0.629
2
)
}
kNm
=
437kNm
>
433kNm
=
M
Ed
and so the design moment resistance is adequate after all.
6.15.5 Example 5 - checking a braced beam by
buckling analysis
Problem
. Use the method of elastic buckling analysis given in Section 6.8.2 to
check the braced beam of Section 6.15.2.
Elastic buckling analysis.
The application of the method of elastic buckling analysis given in Section 6.8.2
is summarised below, using the same step numbering as in Section 6.8.2.
(2) The beam is fully restrained at mid-span, and so consists of two segments
12 and 23.
For segment 12,
M
1
=−
70kNm and
M
2
=
122.5kNm (as in Section
6.15.2).
β
m
12
=
70
/
122.5
=
0.571
Using equation 6.5,
α
m
12
=
1.75
+
1.05
×
0.571
+
0.3
×
0.571
2
=
2.448
<
2.56
For segment 23,
β
m
23
=
0
/
122.5
=
0 and
α
m
23
=
1.75 as in Section 6.15.2
(3)
L
cr
12
=
L
cr
23
=
4500mm.
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